作者electrify (小狼狗)
看板Grad-ProbAsk
標題Re: [理工] [機率]-請問一題
時間Fri Aug 7 10:52:20 2009
※ 引述《msu (do my best)》之銘言：
: Suppose a fair coin is tossed n times.
: Each coin toss costs d dollars and the reward is obtaining X heads is
: 2
: aX +bx Find the expected value of the net reward.
: 請問這題如何解^^
: 感謝~~
: 他答案給
: 1 1 1
: a(---n+---n^2)+b(---n)-nd
: 4 4 2
: 不過我不是很懂他怎如何求的...
P(H) = 1/2
r.v.X ~B(n,p)
n
f(x) = C (1/2)^x * (1/2)^(n-x)
x
E[X] = np = (1/2)*n
Var[X] = np(1-p) =(1/4)*n
E[X^2] = Var[X]+E[X]^2 = (1/4)*n + (1/4)*n^2
y = 贏來的錢 = ax^2+bx-dn
= a[(1/4)*n + (1/4)*n^2] + b[(1/2)*n] - dn
這題我上星期剛做 (￣‥a￣)
有錯請指教 <(_ _)>
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